What does the quote by Anthony Burgess, " a long stripping off of illusion," mean?
The Anthony Burgess quote in question comes from his desire to write novels which provide "a long stripping off of illusion." According to Burgess, all novels which he wrote after A Vision of Battlements (1965) were his attempt to take illusion out of the equation.
Therefore, the quote refers to the fact that time has allowed an illusion to build up on the things around us, so much so that they can no longer be recognized in their natural state. Therefore, Burgess believes that to show life, the illusion of life must be removed. Given that it has taken a very long time for the illusion to be built up, it will take just as long to remove the remnants of the illusion (in order to uncover the reality which lies underneath).
Essentially, Burgess believes that even with realistic texts existing, it may take some time before they are recognized as realistic. Previous texts have colored life to be something very different than it really is. That said, even realistic texts may not be accepted as realistic, given the history of the illusions given to readers in the past.
Burgess recognizes that it will take a long time, "a long stripping off," to show things as they are. Essentially, the novels which followed A Vision of Battlements, beginning with Tremor of Intent: An Eschatological Spy Novel (1966) and ending with Byme: A Novel (1995-published two years after his death) all attempted to continue the stripping of illusion.